Fractional-order shifted Legendre collocation method for solving non-linear variable-order fractional Fredholm integro-differential equations

Abdelkawy M., Amin A. Z. M. A., Lopes A. M.

Computational and Applied Mathematics, vol.41, no.1, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1007/s40314-021-01702-4
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Keywords: Fractional-order Legendre-Gauss-Lobatto, Riemann-Liouville fractional derivative, System of variable-order factional Fredholm integro-differential equations, Variable-order fractional Fredholm integro-differential equation
  • Istanbul Gelisim University Affiliated: No

Abstract

Fractional differential equations have been adopted for modeling many real-world problems, namely those appearing in biological systems since they can capture memory and hereditary effects. In this paper, an efficient and accurate method for solving both one-dimensional and systems of nonlinear variable-order fractional Fredholm integro-differential equations with initial conditions is proposed. The method is based on the fractional-order shifted Legendre–Gauss–Lobatto collocation technique for fractional-order Riemann–Liouville derivative. The effectiveness and validity of the numerical approach are illustrated by solving four distinct problems.